1. Warm Up Simplify each expression by combining like terms. 1. 4x + 2x
2. 3y + 7y
3. 8p – 5p
4. 5n + 6n2
Simplify each expression.
5. 3(x + 4)
6. –2(t + 3)
7. –1(x2 – 4x – 6) 6x
10y 3p
not like terms
3x + 12
–2t – 6
–x2 + 4x + 6

2. Graph the line given the slope and y-intercept.
slope = 4; y-intercept =

3. Learning Target
Students will be able to: Add and subtract polynomials.

4. Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.

5. Add or Subtract..
A. 12p3 + 11p2 + 8p3
D. 10m2n + 4m2n – 8m2n
12p3 + 11p2 + 8p3
10m2n + 4m2n – 8m2n
20p3 + 11p2
6m2n
B. 5x2 – 6 – 3x + 8
E. 2s2 + 3s2 + s
5x2 – 6 – 3x + 8
2s2 + 3s2 + s
5s2 + s
5x2 – 3x + 2
C. t2 + 2s2 – 4t2 – s2
F. 4z4 – z4 + 2
t2 + 2s2 – 4t2 – s2
4z4 – z4 + 2
–3t2 + s2
20z4 – 6

6. Add or subtract.
G. 2x8 + 7y8 – x8 – y8
2x8 + 7y8 – x8 – y8
x8 + 6y8
H. 9b3c2 + 5b3c2 – 13b3c2
9b3c2 + 5b3c2 – 13b3c2
b3c2

7. Polynomials can be added in either vertical or horizontal form.
In vertical form, align the like terms and add:
5x2 + 4x + 1
+ 2x2 + 5x + 2
7x2 + 9x + 3
(5x2 + 4x + 1) + (2x2 + 5x + 2)
= 7x2 + 9x + 3

8. Add.
A. (4m2 + 5) + (m2 – m + 6)
5m2 – m + 11
B. (10xy + x) + (–3xy + y)
7xy + x + y
C. (6x2 – 4y) + (3x2 + 3y – 8x2 – 2y)
x2 – 3y D.

9. Add (5a3 + 3a2 – 6a + 12a2) + (7a3 – 10a).
12a3 + 15a2 – 16a
Distribute.
–(2x3 – 3x + 7)= –2x3 + 3x – 7
Subtract.
(x3 + 4y) – (2x3)
–x3 + 4y

10. Subtract.
(7m4 – 2m2) –(5m4 – 5m2 + 8)
2m4 + 3m2 – 8

11. Subtract.
(–10x2 – 3x + 7) – (x2 – 9)
–11x2 – 3x + 16

12. Subtract.
(9q2 – 3q) – (q2 – 5)

13. Subtract.
(2x2 – 3x2 + 1) – (x2 + x + 1)

14. The profits of two different manufacturing plants can be modeled as shown, where x is the number of units produced at each plant.
Use the information above to write a polynomial that represents the total profits from both plants.
–0.03x2 + 25x – 1500 +
–0.02x2 + 21x – 1700
–0.05x2 + 46x – 3200